RECOMENDACIONES

7.7

Signal to background ratio in

228

Th measure-

ment

Samples of SSE events can be also collected using uncollimated228Th measurements. In the decay chain of 228Th we find 208Tl which emits the most energetic γ-line that can be found in nature with 2614.5 keV. At this energy pair production is the dom- inant process of photon interaction with matter. The positron which is created in this process materializes and subsequently annihilates with an electron emitting two photons back-to-back with an energy of 511 keV each. The photons can escape the detector in which case their energy is missing. Three characteristic lines can be see in

228_{Th spectra. The Full Energy Peak (FEP) of the}208_{Tl line at 2614.5 keV, the Single}

Escape Peak (SEP) at 2103.5 keV and the Double Escape Peak (DEP) at 1592.5 keV.

If both photons escape the detector the remaining energy is released in a very small volume thus events in the DEP are SSE events. The probability of both photons escaping the detector is highest on the detector surface and especially high in its corners. Hence, the spatial distribution of DEP events is very inhomogeneous.

A 228Th measurement was done with the BEGe detector at HV = 5kV with a measurement real time of about 3 h. the distribution of A/E versus the calibrated energy can be seen in Figure 7.15. The SSE events emerge as a horizontal band. To estimate the background contribution in the DEP line we fit the A/E distribution of (1592±5) keV (see Figure 7.16 with a Gaussian fit function and allow for a low energy tail (Equation 4.4). As for the 137_{Cs coincidence measurements, the contribution is}

estimated from the two side bands left and right of the Gaussian; we find a SSE to background ratio of (11759 − 747)/747 = 14.7 ± 0.6.

Figure 7.15: A/E versus calibrated energy of a228_{Th measurement recorded}

with the BEGe detector. The SSE events are visible as a horizontal band and the DEP with the highest SSE contribution at an energy of 1592 keV.

7.7. Signal to background ratio in 228Th measurement

The tail was not observed in the A/E distribution of the 137Cs measurement in Fig- ure 7.2 and the SSE to background ratio achieved with the 137_{Cs measurements is}

always higher except for Run4, Run5 and Run15 (see Table 7.2). Note that these measurements were central scans and the contribution of SSE events from the de- tector center in a 228_{Th measurement is negligible. The best SSE to background}

ratio estimated is 121.4 ± 31.7 in Run17.

Figure 7.16: 228Th A/E distribution of the DEP line. A Gaussian plus low energy tail fit is shown in red. The two side bands used to estimate the SSE to background ratio are shown as gray bands.

Chapter 8

Analysis of the background

component

42

Ar in Gerda

As already mentioned in Chapter 2 background control is essential for low back- ground experiments. All contributions have to be understood in order to minimize and estimate them. One important background component in Gerda is the β con- tinuum of42_{K, daughter of}42_{Ar which is naturally present in the cryo liquid Argon}

(LAr) of the Gerda setup.

8.1

Production mechanism of

42

Ar

The abundance of42_{Ar in natural liquid Argon depends on the way}42_{Ar is produced.}

So in order to get a feeling of the order of magnitude of the specific activity of42_Ar

we look for its production mechanisms.

As pointed out in [68] 42_{Ar can be produced via double neutron capture by} 40_Ar 40_{Ar + n −→} 41_{Ar + n −→} 42_{Ar (8.1)}

They estimate the natural 42Ar abundance from both naturally occurring neutrons and neutrons which are produced in nuclear explosions and come to an estimate of 42_Ar/40_{Ar = 7.4 · 10}−22 _{corresponding to A(}42_{Ar) = 7.4 µBq/kg for the latter as}

dominant mechanism.

However, they do not consider the cosmic-ray production of 42_{Ar in the upper at-}

mosphere via the reaction

40_{Ar + α −→} 42_{Ar + 2 p (8.2)}

which could be about three orders of magnitude higher and therefore the main production mechanism for 42_{Ar [69]. The authors estimate the ratio} 42_Ar/40_Ar

to be roughly 10−20 in the atmosphere. This would correspond to an activity of A(42_{Ar) ≈ 100 µBq/kg (see Appendix F). The assumptions made in both references}

are more of qualitative nature though and the calculated values can only be rough estimates.

8.2. Previous measurements

8.2

Previous measurements

Before the neutrinoless double beta decay experiment Gerda was built, a pro- posal [70] was made in which an upper limit of the 42Ar specific activity in LAr of 43 µBq/kg [71] is stated (see also Appendix F). This value would suggest a lower cross section for cosmic-ray production of42_{Ar as assumed by [69]. Now that Gerda}

has concluded Phase I data taking, this value can be checked. In fact first tests re- vealed that the background from 42_{Ar was a lot higher than expected from the pro-}

posal and efforts were made to reduce this background by deploying Mini-Shrouds in the Gerda setup. A Mini-Shroud is a closed copper cylinder which encloses a de- tector string in order to minimize the quantity of42_{Ar in contact with the detectors}

and to close the electric field lines.

8.3

Methodology

42_{Ar decays via β}− _{decay to}42_{K which further decays to} 42_{Ca via another β}− _decay

with an endpoint of 3525.45 keV (see Figure 8.1 and Figure 8.2).

As the energy spectrum of electrons from a beta decays is continuous, this decay contributes also at lower energies to the background especially in the region of interest around Q0ν

ββ= 2039 keV.

Figure 8.1: Decay scheme of 42_{Ar taken from [72].}

8.4. Distribution of 42K All other unstable isotopes of Argon apart from 42Ar can be neglected as source of background around Q0ν

ββ because either their lifetime is short and they have al-

ready decayed, e.g. 41_{Ar has a lifetime of ca. 110 min, or the endpoint energy of the}

decay Qββis lower than Q0νββ, e.g. 39Ar has an endpoint energy of Qββ = 565 keV [73].

The Gerda LAr has been underground since November 2007. With the lifetime of 42_{Ar being ((32.9 ± 1.1) )y (measured in 1965) [74] and the lifetime of} 42_{K being}

((12.360 ± 0.01) )y, they are in secular equilibrium. This means the specific activity of 42Ar and 42K are the same.

In the following the specific activity of42Ar is calculated by estimating the activity of

42_{K using almost all Gerda Phase I data. We use a γ-line of the}42_{K spectrum which}

has an energy of (1524.65 ± 0.03) keV and perform a binned maximum likelihood fit using the Bayesian Analysis Toolkit (BAT) [75]. Finally the calculated specific activity is corrected for the half life of 42_{Ar in order to be comparable to other}

measurements and theoretical values and limits.

8.4

Distribution of

42

K

To estimate the specific activity of42_{K in the Gerda LAr we have to make assump-} tions about its distribution inside the LAr and here it starts to become tricky: As

42_{K is born in a β}− _{decay it is born as a positive ion namely as}42_K+_{. The detectors}

are operated at high voltage (HV), typically with 4 kV inverse bias, which creates strong electric fields and under the influence of electric fields ions are drifted. With- out further measures the distribution of42_{K would surely be inhomogeneous.}

A lot of effort was put in making most of the LAr volume as field-free as possible by deploying small, electrically grounded copper cylinders around the detectors and by shielding the HV cables. These so called Mini-Shrouds (MS) additionally form a physical barrier for 42_K+ _ions.

8.5

Efficiencies

The detection efficiency is a very crucial ingredient in the activity determination as it is fully anti correlated to the specific activity itself. It is determined with a Monte Carlo Simulation assuming a specific distribution of42_{Ar in LAr inside Gerda. The}

simulation program we use is called MaGe; it is Geant4 based and is developed by the Gerda and Majorana experiments in a collaborative effort [66, 76].

8.5.1

Simulation

The Gerda setup (see Section 2) is available as MaGe [66] geometry for MC simu- lations. A cylinder of 42K decays was simulated centered on the respective detector string. It has to be large enough in order not to miss important contributions to

8.5. Efficiencies

the efficiency of the detectors. A height of 2.10 m and a radius of 1 m were chosen according to a previous study [77]. In the following we call the incident simulated particles primaries and their starting position the primary vertex.

In Figure 8.3 all primaries are plotted that deposit energy in at least one of the detectors. The simulation contains only the one string arm in the configuration starting from Run34 (see Appendix G). Decays outside the simulated volume are considered in the systematic uncertainty (see Section 8.11).

The simulated volume was split in four parts as can be seen in Figure 8.4. The top, bottom and tube volumes combined are the volume simulated outside the respective Mini-Shroud (MS). The distribution of decays inside the MS can be varied to study systematic effects on the efficiency. Afterwards, the simulations from inside the MS and those from outside the MS can be combined without re-simulating the outer part which stays the same. Also, higher statistics are achieved in this manner.

Figure 8.3: Vertex positions of primaries which deposit energy in at least one of the BEGe detectors.

Figure 8.4: LAr cylinder in which 42_{K decays are simulated. The cylinder}

is split in four separate volumes in order to be able to simulate different distributions inside the Mini-Shroud (MS) and combine them later.

8.5. Efficiencies

In each of the above said volumes a total number of 109 decays were simulated using Decay0 [78] to create the primary vertices in order to account for correlations in γ cascade emissions. The spectrum of primary particles is plotted in Figure 8.5.

As a crosscheck of the Monte Carlo simulation a rough estimate of the branching ratio RB(1525 keV) of the 1525 keV γ-line was performed. From 1500 keV to 1550 keV

the spectrum is binned in 51 bins. Dividing in three regions of equal size we estimate the background using the side bands and subtract it from the middle region which contains the γ-line.

RB(1525 keV) = P34 i=18ni− P17 i=1ni+ P51 i=35ni
Ntot = (18.071 ± 0.001) · 10−2 (8.3)

The number of entries in bin i is denoted as ni and Ntot is the total number of

simulated decays. The calculated value is in accordance with the literature value of Rlit

B(1525 keV) = (18.08 ± 0.09) · 10

−2 _[72].

8.5.2

Efficiency calculation

In order to calculate the efficiency of the detectors in the Gerda setup to detect a 1525 keV γ photon from a 42_{K decay inside the LAr we first calculate the signal}

counts in said γ-line from the output spectra of the simulations. The efficiency is then calculated as the number of signal counts divided by the total number of simulated decays. Last, the efficiencies are normalized by the simulated LAr volume and expressed as the rate per day seen for a specific activity of 1 µBq/kg.

Figure 8.5: Primary spectrum of the efficiency simulations containing 107

8.5. Efficiencies

To extract the signal counts, the energy window [1499 keV,1550 keV] of the simu- lation output spectra is subdivided in three regions of same size. B1 and B2 are

the sidebands and M denotes the middle region which contains the 42_{K γ-line at}

≈ 1525 keV which we use to estimate the specific activity of 42_{Ar. Using the two}

side bands we estimate the background contribution in region M and calculate the signal counts S as follows

S = M − 1

2(B1+ B2) (8.4) We calculate the efficiency ε by dividing S by the number of simulated decays Nsim

ε = S Nsim

(8.5)

To estimate the uncertainty on the efficiency we have to take the branching ratio RB

of the 1525 keV line into account. Effectively we are not calculating the efficiency on the full decay but on the 1525 keV line which we will denote as ε15

ε15=

S Nsim· RB

(8.6)

The uncertainty, which is calculated using binomial statistics, is then

∆ε15=

s

ε15(1 − ε15)

Nsim· RB

(8.7)

The uncertainty on the total efficiency ε is therefore

∆ε = s  ∂ε ∂ε15 · ∆ε15 2 +  ∂ε ∂RB · ∆RB 2 (8.8) ∆ε ε = s  ∆ε15 ε15 2 + ∆RB RB 2 (8.9)

If we neglect the uncertainty on the branching ratio ∆RB for Nsim → ∞ this tends

to ∆ε ε ≈ ∆ε15 ε15 = s ε15(1 − ε15) Nsim· RB· ε215 = r (1 − ε15) S Nsim→∞ −→ √1 S (8.10) With RB = 0.1808 ± 0.009 [72] and ∆ε/ε ≈ 10−2 though, the uncertainty on the

branching ratio can not simply be neglected but contributes with approximately 10 % to the total uncertainty. In the following ∆ε contains this contribution. In the final analysis the efficiency enters as the rate per day which is seen by the respective detector for an 42_{Ar activity of 1 µBq/kg. Therefore, we define the normalized}

efficiency εn as

εn = ε · mLAr· fn (8.11)

With the LAr mass mLAr given by the density of LAr ρLAr = 1.39 g/cm 3

multiplied by its volume VLAr:

8.5. Efficiencies

and the normalization factor

fn = 1 µBq kg · 8.64 · 10 4 s d = 8.64 · 10 −2 decays kg d (8.13)

Efficiencies of complementary simulations i can be combined by simply summing them up if there is no overlap of the simulated LAr volume and if they are normalized

En= Σiεn,i (8.14)

Supposing that complementary simulations are uncorrelated we add up the uncer- tainties on the single efficiencies in quadrature to obtain the combined uncertainty

Ξn =

q

Σi∆ε2n,i (8.15)

All simulations with their normalization factors are listed in Table 8.1. In order to ensure that the volume splitting, which was described in Section 8.5.1, leads to a reasonable result for the efficiencies, for detector string 3 (S3) a simulation without volume splitting as well as with volume splitting was done. S3 contains three detectors; their efficiencies for the split simulation and the full volume simulation are compared in Table 8.2.

Table 8.1: List of simulations and normalization factors. The normalization factor for inhomogeneous distributions inside the MS is the same as for the homogeneous distribution because a priori we do not know the real distribution and assume a homogeneous one.

# string position V [cm3_{] m [kg] m · f} n 1 S1 top 2543330 3535 305.444 2 S1 bottom 2544630 3537 305.600 3 S1 tube 1500070 2085 180.152 4 S1 hom 3285.45 4.57 0.395

5 S1 near BEGe hom

6 S1 near MS hom 7 S2 all 6591250 9162 791.583 8 S3 all 6591360 9162 791.596 9 S3 top 2543320 3535 305.443 10 S3 bottom 2544630 3537 305.600 11 S3 tube 1500600 2086 180.216 12 S3 hom 2746.51 3.82 0.330

13 S3 near BEGe hom

14 S3 near MS hom

15 S4 all 6591280 9162 791.586 16 S1 AC 6591070 9162 791.561

8.5. Efficiencies

Table 8.2: Comparison of complete (all) and split efficiency simulations (hom). The split simulation has four different volume parts which are added like described in Equation 8.14. The difference ∆ = (εn(hom) −

εn(all))/εn(hom) is well within the uncertainty bounds.

hom all

name εn [10−3/d] εn [10−3/d] ∆[%]

RGI 3.75 ± 0.03 3.75 ± 0.06 -0.08 ANG4 4.27 ± 0.03 4.20 ± 0.06 1.64

RGII 3.90 ± 0.03 3.86 ± 0.06 1.01

Table 8.3: Efficiencies of all Phase I detectors with the list of simulations which were combined to calculate them. The values indicated with hom are used as central value and the nearDet and nearMS values are used to estimate a systematic uncertainty due to the inhomogeneity of 42_{K decays}

(see Section 8.11).

hom nearDet nearMS

name εn [10−3/d] εn [10−3/d] εn [10−3/d] sim list

GD32B 1.03 ± 0.01 1.01 ± 0.01 0.94 ± 0.01 1-6 GD32C 1.10 ± 0.01 1.22 ± 0.01 1.02 ± 0.01 1-6 GD32D 1.07 ± 0.01 1.19 ± 0.01 0.98 ± 0.01 1-6 GD35B 1.20 ± 0.01 1.32 ± 0.01 1.12 ± 0.01 1-6 GD35C 0.87 ± 0.01 0.87 ± 0.01 0.80 ± 0.01 1-6 ANG3 4.23 ± 0.06 - - 15 ANG5 5.24 ± 0.07 - - 15 RGIII 4.08 ± 0.06 - - 15 RGI 3.75 ± 0.03 3.57 ± 0.03 3.59 ± 0.03 9-14 ANG4 4.27 ± 0.03 4.81 ± 0.03 4.10 ± 0.03 9-14 RGII 3.90 ± 0.03 3.97 ± 0.03 3.77 ± 0.03 9-14 GTF112 6.15 ± 0.08 - - 7 ANG2 5.43 ± 0.07 - - 7 ANG1 1.44 ± 0.03 - - 7 GTF45 5.02 ± 0.07 - - 16 GTF32 4.83 ± 0.07 - - 16

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